Is polymath a good investment3/31/2024 ![]() Our results also apply to the more general setting of matroids.Įarlier the best result was giving disjoint transversal bases. In this paper we prove that one can always find $\left(1/2-o\left(1\right)\right)n$ disjoint transversal bases, improving on the previous best bound of $\Omega\left(n/\log n\right)$. Rota’s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (for example, the conjecture was recently the subject of the collaborative “Polymath” project). ![]() Given $n$ bases $B_$ (we call such bases transversal bases). Halfway to Rota’s basis conjecture, by Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, and Benny SudakovĪbstract: In 1989, Rota made the following conjecture. Three short items: Progress on Rota’s conjecture (polymath12) by Bucić, Kwan, Pokrovskiy, and Sudakovįirst, there is a remarkable development on Rota’s basis conjecture ( Polymath12) described in the paper
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